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During the pandemic, I learned about Hitomezashi, a Japanese stitching pattern with rows and columns of alternating stitch-no-stitch line segments. You can generate them randomly by tossing a coin for each row and column, determining stitch-no-stitch-stitch or no-stitch-stitch-no-stitch patterns. The first image is generated using this website https://hitomezashi.com.
Yesterday, I wondered what it would look like in a radial pattern. The other two pictures are constructed similarly but along rays and concentric circles.
I also saw that Katherine Seaton has a book coming out on this topic in December! https://x.com/maths_kath/status/1823308557493940253
@OscarCunningham @divbyzero for a spherical-geometry version you could start with an icosidodecahedron.
Or, more generally, take a set of great circles on a sphere with no three meeting at a point. Then you'd be guaranteed that all vertices had degree 4 and that each circle had an even number of segments.
I don't have a convenient 3d modelling tool to throw together an example right now, though!